ترغب بنشر مسار تعليمي؟ اضغط هنا

Siegel-Veech constants for strata of moduli spaces of quadratic differentials

179   0   0.0 ( 0 )
 نشر من قبل Elise Goujard
 تاريخ النشر 2014
  مجال البحث
والبحث باللغة English
 تأليف Elise Goujard




اسأل ChatGPT حول البحث

We present an explicit formula relating volumes of strata of meromorphicquadratic differentials with at most simple poles on Riemann surfacesand counting functions of the number of flat cylinders filled by closedgeodesics in associated flat metric with singularities. This generalizes the resultof Athreya, Eskin and Zorich in genus 0 to higher genera.



قيم البحث

اقرأ أيضاً

161 - Alex Eskin , Anton Zorich 2015
We state conjectures on the asymptotic behavior of the volumes of moduli spaces of Abelian differentials and their Siegel-Veech constants as genus tends to infinity. We provide certain numerical evidence, describe recent advances and the state of the art towards proving these conjectures.
136 - Elise Goujard 2015
The volumes of strata of Abelian or quadratic differentials play an important role in the study of dynamics on flat surfaces, related to dynamics in polygonal billiards. This article reviews all known ways to compute volumes in the quadratic case and provides explicit values of volumes of the strata of meromorphic quadratic differentials with at most simple poles in all low dimensions.
145 - Max Bauer 2014
An Abelian differential gives rise to a flat structure (translation surface) on the underlying Riemann surface. In some directions the directional flow on the flat surface may contain a periodic region that is made up of maximal cylinders filled by p arallel geodesics of the same length. The growth rate of the number of such regions counted with weights, as a function of the length, is quadratic with a coefficient, called Siegel-Veech constant, that is shared by almost all translation surfaces in the ambient stratum. We evaluate various Siegel-Veech constants associated to the geometry of configurations of periodic cylinders and their area, and study extremal properties of such configurations in a fixed stratum and in all strata of a fixed genus.
A $k$-differential on a Riemann surface is a section of the $k$-th power of the canonical line bundle. Loci of $k$-differentials with prescribed number and multiplicities of zeros and poles form a natural stratification of the moduli space of $k$-dif ferentials. In this paper we give a complete description for the compactification of the strata of $k$-differentials in terms of pointed stable $k$-differentials, for all $k$. The upshot is a global $k$-residue condition that can also be reformulated in terms of admissible covers of stable curves. Moreover, we study properties of $k$-differentials regarding their deformations, residues, and flat geometric structure.
Let S be a closed topological surface. Haupts theorem provides necessary and sufficient conditions for a complex-valued character of the first integer homology group of S to be realized by integration against a complex-valued 1-form that is holomorph ic with respect to some complex structure on S. We prove a refinement of this theorem that takes into account the divisor data of the 1-form.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا